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<H3>fix balance command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID balance Nfreq dimstr Niter thresh keyword value ... 
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command 

<LI>balance = style name of this fix command 

<LI>Nfreq = perform dynamic load balancing every this many steps 

<LI>dimstr = sequence of letters containing "x" or "y" or "z", each not more than once 

<LI>Niter = # of times to iterate within each dimension of dimstr sequence 

<LI>thresh = stop balancing when this imbalance threshhold is reached 

<LI>zero or more keyword/arg pairs may be appended 
</UL>
<LI>keyword = <I>out</I> 

<PRE> <I>out</I> arg = filename
   filename = output file to write each processor's sub-domain to 
</PRE>

</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 2 all balance 1000 x 10 1.05
fix 2 all balance 0 xy 20 1.1 out tmp.balance 
</PRE>
<P><B>Description:</B>
</P>
<P>This command adjusts the size of processor sub-domains within the
simulation box dynamically as a simulation runs, to attempt to balance
the number of particles and thus the computational cost (load) evenly
across processors. The load balancing is "dynamic" in the sense that
rebalancing is performed periodically during the simulation.  To
perform "static" balancing, before of between runs, see the
<A HREF = "balance.html">balance</A> command.
</P>
<P>Load-balancing is only useful if the particles in the simulation box
have a spatially-varying density distribution.  E.g. a model of a
vapor/liquid interface, or a solid with an irregular-shaped geometry
containing void regions. In this case, the LAMMPS default of dividing
the simulation box volume into a regular-spaced grid of processor
sub-domain, with one equal-volume sub-domain per procesor, may assign
very different numbers of particles per processor. This can lead to
poor performance in a scalability sense, when the simulation is run in
parallel.
</P>
<P>Note that the <A HREF = "processors.html">processors</A> command gives you some
control over how the box volume is split across
processors. Specifically, for a Px by Py by Pz grid of processors, it
lets you choose Px, Py, and Pz, subject to the constraint that Px * Py
* Pz = P, the total number of processors. This can be sufficient to
achieve good load-balance for some models on some processor
counts. However, all the processor sub-domains will still be the same
shape and have the same volume.
</P>
<P>This command does not alter the topology of the Px by Py by Pz grid or
processors. But it shifts the cutting planes between processors (in
3d, or lines in 2d), which adjusts the volume (area in 2d) assigned to
each processor, as in the following 2d diagram. The left diagram is
the default partitioning of the simulation box across processors (one
sub-box for each of 16 processors); the right diagram is after
balancing.
</P>
<CENTER><IMG SRC = "JPG/balance.jpg">
</CENTER>
<P>IMPORTANT NOTE: This command attempts to minimize the imbalance
factor, as defined above.  But because of the topology constraint that
only the cutting planes (lines) between processors are moved, there
are many irregular distributions of particles, where this factor
cannot be shrunk to 1.0, particuarly in 3d.  Also, computational cost
is not strictly proportional to particle count, and changing the
relative size and shape of processor sub-domains may lead to
additional computational and communication overheads, e.g. in the PPPM
solver used via the <A HREF = "kspace_style.html">kspace_style</A> command.  Thus
you should benchmark the run times of your simulation with and without
balancing.
</P>
<HR>

<P>The <I>group-ID</I> is currently ignored.  In the future it may be used to
determine what particles are considered for balancing.  Normally it
would only makes sense to use the <I>all</I> group.  But in some cases it
may be useful to balance on a subset of the particles, e.g. when
modeling large nanoparticles in a background of small solvent
particles.
</P>
<P>The <I>Nfreq</I> setting determines how often a rebalance is performed.  If
<I>Nfreq</I> > 0, then rebalancing will occur every <I>Nfreq</I> steps.  Each
time a rebalance occurs, a reneighboring is triggered, so you should
not make <I>Nfreq</I> too small.  If <I>Nfreq</I> = 0, then rebalancing will be
done every time reneighboring normally occurs, as determined by the
the <A HREF = "neighbor.html">neighbor</A> and <A HREF = "neigh_modify.html">neigh_modify</A>
command settings.
</P>
<P>On rebalance steps, rebalancing will only be attempted if the current
imbalance factor, as defined above, exceeds the <I>thresh</I> setting.
</P>
<P>The <I>dimstr</I> argument is a string of characters, each of which must be
an "x" or "y" or "z".  Eacn character can appear zero or one time,
since there is no advantage to balancing on a dimension more than
once.  You should normally only list dimensions where you expect there
to be a density variation in the particles.
</P>
<P>Balancing proceeds by adjusting the cutting planes in each of the
dimensions listed in <I>dimstr</I>, one dimension at a time.  For a single
dimension, the balancing operation (described below) is iterated on up
to <I>Niter</I> times.  After each dimension finishes, the imbalance factor
is re-computed, and the balancing operation halts if the <I>thresh</I>
criterion is met.
</P>
<P>A rebalance operation in a single dimension is performed using a
density-dependent recursive multisectioning algorithm, where the
position of each cutting plane (line in 2d) in the dimension is
adjusted independently.  This is similar to a recursive bisectioning
(RCB) for a single value, except that the bounds used for each
bisectioning take advantage of information from neighboring cuts if
possible, as well as counts of particles at the bounds on either side
of each cuts, which themselves were cuts in previous iterations.  The
latter is used to infer a density of pariticles near each of the
current cuts.  At each iteration, the count of particles on either
side of each plane is tallied.  If the counts do not match the target
value for the plane, the position of the cut is adjusted based on the
local density.  The low and high bounds are adjusted on each
iteration, using new count information, so that they become closer
together over time.  Thus as the recustion progresses, the count of
particles on either side of the plane gets closer to the target value.
</P>
<P>The density-dependent part of this algorithm is often an advantage
when you rebalance a system that is already nearly balanced.  It
typically converges more quickly than the geometric bisectioning
algorithm used by the <A HREF = "balance.html">balance</A> command.  However, if can
be a disadvants if you attempt to rebalance a system that is far from
balanced, and converge more slowly.  In this case you probably want to
use the <A HREF = "balance.html">balance</A> command before starting a run, so that
you begin the run with a balanced system.
</P>
<P>Once the rebalancing is complete and final processor sub-domains
assigned, particles migrate to their new owning processor as part of
the normal reneighboring procedure.
</P>
<P>IMPORTANT NOTE: At each rebalance operation, the RCB operation for
each cutting plane (line in 2d) typcially starts with low and high
bounds separated by the extent of a processor's sub-domain in one
dimension.  The size of this bracketing region shrinks based on the
local density, as described above, which should typically be 1/2 or
more every iteration.  Thus if <I>Niter</I> is specified as 10, the cutting
plane will typically be positioned to better than 1 part in 1000
accuracy (relative to the perfect target position).  For <I>Niter</I> = 20,
it will be accurate to better than 1 part in a million.  Thus there is
no need to set <I>Niter</I> to a large value.  This is especially true if
you are rebalancing often enough that each time you expect only an
incremental adjustement in the cutting planes is necessary.  LAMMPS
will check if the threshold accuracy is reached (in a dimension) is
less iterations than <I>Niter</I> and exit early.
</P>
<P>IMPORTANT NOTE: If a portion of your system is a perfect lattice,
e.g. a frozen substrate, then the balancer may be unable to achieve
exact balance.  I.e. entire lattice planes will be owned or not owned
by a single processor.  So you you should not expect to achieve
perfect balance in this case.  Nor will it be helpful to use a large
value for <I>Niter</I>, since it will simply cause the balancer to iterate
until <I>Niter</I> is reached, without improving the imbalance factor.
</P>
<HR>

<P>The <I>out</I> keyword writes a text file to the specified <I>filename</I> with
the results of each rebalancing operation.  The file contains the
bounds of the sub-domain for each processor after the balancing
operation completes.  The format of the file is compatible with the
<A HREF = "pizza">Pizza.py</A> <I>mdump</I> tool which has support for manipulating and
visualizing mesh files.  An example is shown here for a balancing by 4
processors for a 2d problem:
</P>
<PRE>ITEM: TIMESTEP
1000
ITEM: NUMBER OF SQUARES
4
ITEM: SQUARES
1 1 1 2 7 6
2 2 2 3 8 7
3 3 3 4 9 8
4 4 4 5 10 9
ITEM: TIMESTEP
1000
ITEM: NUMBER OF NODES
10
ITEM: BOX BOUNDS
-153.919 184.703
0 15.3919
-0.769595 0.769595
ITEM: NODES
1 1 -153.919 0 0
2 1 7.45545 0 0
3 1 14.7305 0 0
4 1 22.667 0 0
5 1 184.703 0 0
6 1 -153.919 15.3919 0
7 1 7.45545 15.3919 0
8 1 14.7305 15.3919 0
9 1 22.667 15.3919 0
10 1 184.703 15.3919 0 
</PRE>
<P>The "SQUARES" lists the node IDs of the 4 vertices in a rectangle for
each processor (1 to 4).  The first SQUARE 1 (for processor 0) is a
rectangle of type 1 (equal to SQUARE ID) and contains vertices
1,2,7,6.  The coordinates of all the vertices are listed in the NODES
section.  Note that the 4 sub-domains share vertices, so there are
only 10 unique vertices in total.
</P>
<P>For a 3d problem, the syntax is similar with "SQUARES" replaced by
"CUBES", and 8 vertices listed for each processor, instead of 4.
</P>
<P>Each time rebalancing is performed a new timestamp is written with new
NODES values.  The SQUARES of CUBES sections are not repeated, since
they do not change.
</P>
<HR>

<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
files</A>.  None of the <A HREF = "fix_modify.html">fix_modify</A> options
are relevant to this fix.
</P>
<P>This fix computes a global scalar which is the imbalance factor
after the most recent rebalance and a global vector of length 3 with
additional information about the most recent rebalancing.  The 3
values in the vector are as follows:
</P>
<UL><LI>1 = max # of particles per processor
<LI>2 = total # iterations performed in last rebalance
<LI>3 = imbalance factor right before the last rebalance was performed 
</UL>
<P>As explained above, the imbalance factor is the ratio of the maximum
number of particles on any processor to the average number of
particles per processor.
</P>
<P>These quantities can be accessed by various <A HREF = "Section_howto.html#howto_15">output
commands</A>.  The scalar and vector values
calculated by this fix are "intensive".
</P>
<P>No parameter of this fix can be used with the <I>start/stop</I> keywords of
the <A HREF = "run.html">run</A> command.  This fix is not invoked during <A HREF = "minimize.html">energy
minimization</A>.
</P>
<HR>

<P><B>Restrictions:</B> none
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "processors.html">processors</A>, <A HREF = "balance.html">balance</A>
</P>
<P><B>Default:</B> none
</P>
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